Arraying Loudspeaker Systems

By Marty McCann
Copyright 1998

This paper is going to address the issue of combining loudspeakers to increase the area of coverage from that of an individual loudspeaker. The concept is generally referred to as arraying the enclosures. Proper arraying insures even coverage with a minimum of mutual interference, and thus allows the sound system to perform as near to a single source as possible.

When dealing with multiples of loudspeaker enclosures, the main concern is to maintain the integrity of the high frequency devices. The modern highest quality sound reinforcement loudspeaker enclosures exhibit a high frequency horn that offers uniform frequency response with dispersion; they are said to be constant in their directivity or CD for short. There are still a lot of older horns out there that do not have constant directivity, or a well controlled pattern of coverage. These older horns are referred to as exponential radial horns. By exponential we mean that the rate of flare or taper of the horn increases with the square of the distance away from the throat or entry of the horn. Exponential radial horns do not direct the high frequency information very smoothly, with these horns the high frequency coverage is that of a very narrow beam (usually less than 20 degrees) directly on-axis to the horn. The taper or flares rates of the exponential radial horn are too rapid to allow the air molecules carrying the high frequency information to the cling to the side walls of the horn so they can be directed over a wider area of coverage. The reason constant directivity horns do a much better job is that their rates of flare or taper vary as the sound enters the throat area and moves throughout the horn's boundaries, they are said to be multi-taper and multi-flare. It is this variation of conditions within the sidewalls of the horn that allows for the much-improved high fidelity of the loudspeaker system. This paper assumes that the reader is going to utilize constant directivity high frequency devices in the design of the loudspeaker array.

It needs to be mentioned at this time, that all constant directivity horns require a special type of equalization, commonly called CD EQ, to maintain a flat frequency response. When we succeeded in directing the high frequency information into a wider pattern, we subsequently reduced the level of the highs as well. All constant directivity horns have a high frequency roll off rate of -6 dB or more. A compensatory equalization is employed to maintain a flat frequency response. This equalization is part of the systems crossover design. So this paper assumes that the reader will employ loudspeaker systems with constant directivity horns, with the appropriate equalization as the building blocks of the arrays we are going to discuss.

The biggest mistake or improper application involving systems with constant directivity horns is that when some individuals use them in multiples, they don't take into account the individual coverage patterns and therefore allow the high frequency devices (horns) to overlap in their areas of coverage. Some small or very modest amount of overlap is sometimes necessary and acceptable. However, severe overlapping of coverage (more than 10 degrees) results in interference patterns commonly called lobbing or fingering of the pattern. Remember sound is propagated through the medium of air by the vibrations of the individual air molecules bumping into one another in a pattern that exhibits a wave through the atmosphere. When air molecules bump into one another there is a reaction. For every action is there is an equal and opposite reaction (Sir Isaac Newton). If two billiard balls are traveling at an angle toward the center of a pool table, and are allowed to collide, will they not bounce off of each other at the same angle of their collision? What would make you think that solid air molecules would react any differently? The angle of incidence is equal to the angle of coincidence, or the angle of arrival is equal to the angle of departure.

It is the high frequency information that contains those components of speech that allows us to distinguish the consonant and sibilant sounds that make speech intelligible. Those portions of speech created with the lips and tongue are most important if the system is to have clarity, transparency, and general intelligibility. The word sibilance almost defines itself by the mere pronunciation of the word. It is the sibilant components of speech that allow us to distinguish words from another, words like float, tote, boat, and moat, or dog, log, and frog as examples. If the high frequency information is to be most transparent, i.e., intelligible, multiple loudspeakers must be placed with forethought as to the manner in which the horns will combine to retain the concept of constant directivity of the high frequencies emanating from the array of individual loudspeaker components.

Some definitions first. The Direct Field is that sound field emanating directly from a source and not significantly influenced by any of the boundaries within the room or acoustic space. Since all rooms have boundaries in the form of the ceiling, floor, and walls, eventually some sound will arrive at those surfaces. When sound strikes a solid surface, some small amount sound energy is absorbed due to the friction or heat created in the encounter with the boundary, but the majority of the energy is reflected off of the boundary. This reflected energy is called reverberation or the reverberant sound field, meaning that it is independent and no longer part of the direct field. The first concept I want to express then is that; any direct field that does not arrive at the ear of the listener is wasted energy. In other words, it is best to minimize that sound energy that arrives at the room's surface boundaries. Acoustic energy that does not reach the listener is wasted energy. So the first concept is, "Point the loudspeaker at the audience or congregation, and they will hear it better" (what a concept!). I am continuously amazed by the number of systems installed in churches and auditoriums where the directional components (high frequency horns) are not even directed to the listener's ear at all.

The next definition is for Critical Distance. Critical Distance is that point within a room or acoustic space where the level of the reverberant energy field and the level of the direct sound field are equal. Once you step beyond the point of critical distance, the reverberant level is greater than the direct sound level. The farther you move beyond the critical distance point, the reverberant field tends to mask or cover the direct field. A fairly simple and straightforward test can be conducted in any church to ascertain the approximate point of critical distance in any church sanctuary. You see the church has a critical distance point within its acoustical space, with and without the sound system turned on. It is a good idea to establish the point of critical distance without the sound system first, then conduct the same test employing the sound reinforcement system. The properly installed sound system should move the natural (unassisted) point of critical distance dramatically further out into the listening area. However don't be too surprised if after conducting both the assisted and unassisted tests, if the assisted or reinforced test exhibits an even shorter critical distance measurement. If this is the case, the sound system is of an inappropriate design for that room.

Finding the critical distance point in the church sanctuary can be done with one person acting as the speaking source and two to four subjects acting as the listeners. With the sound system off, have the speaker read a passage from the Bible while standing at the pulpit. (Note: It is best to use a speaker with a normal voice, like the actor, Richard Harris, who has a trained voice projected from the diaphragm and would be more easily understood at a distance than a normal talker.) Have the listeners stand a couple of feet in front of the pulpit, have them listen to the person speaking without looking directly at them (keep their eyes directed), and have them slowly back up the center aisle of the church. Instruct the listeners to raise their hands when they perceive that sound is no longer coming directly from the direction of the person speaking. As you slowly back away there will be a point at which the sound is still understood but it no longer appears to come directly from the source, it just appears to be there. If the listeners are of normal binaural hearing, i.e., both ears work equally well, they should come to within 12 to 18 inches of agreement as to the point in the room where the sound no longer appears to come from the pulpit. After this point is determined, turn on the sound system and repeat the test while speaking into the pulpit microphone. If the system is designed well, there should be a much greater distance from the pulpit to the critical distance point with speech reinforcement. Experiment with this test as it can show you a lot about the acoustics of your church sanctuary and the degree to which your existing sound system is effective.

Before I continue this paper on loudspeaker placement within an array, I would suggest that you read the article on decibels in this publication, as it will prepare you for the following discussion. It would be impossible to address or cover every possible variation of church sanctuaries, so the following information is meant to be used as a guideline as to what to take into account when arraying individual loudspeaker components. There are some small church sanctuaries that can be accommodated by a single loudspeaker enclosure. Usually such a sanctuary is not very deep and not too wide, and a single loudspeaker can indeed cover the majority of the congregation.

The aspect ratio of such a room
Check out the aspect ratio of such a room:
In this case the loudspeaker enclosure has a ninety-degree horizontal angle of coverage as far as the high frequency horn's coverage capability. Notice that it doesn't cover the entire first pew on the left and right sides. This may be acceptable because the members of the congregation seated there could probably hear and understand a sermon delivered from the pulpit without a sound system. If, however, in some room of similar dimension, it is deemed necessary to cover this small zone, that is not in the main FOH (Front of House) systems pattern of coverage; the way to go about this is with what are referred to as near field "fill speakers."

The Peavey Impulse Six would do a good job in this instance. When employing a fill loudspeaker, the power amplifier driving these speakers must have the ability to set the gain or level for these speakers. The proper adjustment is to have the level all the way down, have a listener sit in the area to be covered, and slowly increase the level of the gain control of the amplifier until it is just noticeable that the speaker is on.

A fill loudspeaker by virtue of it's intended use should not be so in level that anyone seated outside the intended area of coverage can tell that the "fill" loudspeaker is on.

A small church angle of coverage
Another consideration in a small church such as this is the angle of coverage in the vertical plane that the loudspeaker offers. Many of our enclosures have a nominal ninety-degree horizontal by a forty-five degree vertical angle of coverage. A typical coverage pattern with a single loudspeaker with a forty-five degree vertical angle of coverage is shown below:

40 ft long by 25 ft wide by 16 ft high
The room in these examples is 40 ft. long by 25 ft. wide by 16 ft. high.

What happens when the room is much longer and a single loudspeaker enclosure does not have enough vertical coverage pattern to do the job? The answer is to employ two enclosures, one for the Far Field and one for the Near Field. The Inverse Square Law says that the direct sound field emanating from a sound source will vary in level with the inverse of the square of the distance away from the source. Or on the decibel scale it becomes simpler, as sound drops in level -6 dB, each time you double the distance away from the source.

A loudspeaker that is intended to cover the first one-third
The important thing to consider here is that the loudspeaker that is intended to cover the first one-third of the congregation must be reduced in level.

Some people recognize the need for two loudspeakers to provide the proper coverage but fail to adjust the level of the amplifier channels that are driving each loudspeaker system. If the Near Field loudspeaker enclosure is not calibrated to be 6 dB lower than the Far Field enclosure, the Near Field enclosure will be the one to feedback first and limit the gain of the whole system.

I will remind you once again the concept here is to try to get as much of the audience within the pattern of the loudspeaker array, while trying to minimize wasted energy that is not reaching the congregations ears directly.

What if the room is even longer still? There is a point where trying to cover a large number of seats from a single cluster of source becomes much more difficult or even impossible. How far can one of these single enclosures throw with a 90 degree by 45 degree high frequency constant directivity horn? The answer depends on several variables, such as room acoustics, program material, and the actual distances involved. Most of our two-way loudspeaker enclosures designed for FOH (Front of House) sound reinforcement can do a good job up to 50 ft. or more. Under certain more ideal acoustical

Conditions, they may still perform well at 60 to 70 ft., but I can't tell you that you would be satisfied with their performance at distances beyond 80 - 100 ft., let alone at 150 ft. or even greater distances.

In times past and present, some sound engineers have employed what are called long-throw horns to increase the coverage with distance. These so-called long throw devices are far from perfect. Often, to provide the necessary sound pressure level at the farthest distances, they are operated at levels that are so high that they interfere with the array's ability to provide even coverage in the first place.

No matter how you slice it, sound drops in level -30 dB at 105 ft. (32 meters). (20 log D1 / D2 = 20 log 32 / 1 = 20 x 1.505 = -30.1 dB) or (20 log 105 / 3.28 = 20 log 32 = -30.1 dB). If the main FOH system has to be so loud in level as to cause pain to the listeners close to the front, what then are they accomplishing? There becomes a point where the best course of action is to use properly delayed loudspeaker systems to cover the rear of the audience. Until recent years, the digital delay lines were of too poor a quality to do the job effectively. This is no longer the case, and delayed loudspeaker systems are becoming more and more the viable solution to the problem of proper coverage with great distances.

In order to understand how the properly delayed remote loudspeaker works, you must know about the propagation of sound itself. Sound travels at a speed of approximately 1130 feet per second. In milliseconds that is 1.13 feet per millisecond (a millisecond is 0.001 seconds). In milliseconds per foot this becomes 0.885 or roughly 0.9 milliseconds per foot. So if you want to place a delayed remote loudspeaker system in a room and calibrate the delay to the arrival time of the FOH system, you would measure the distance between the main and delayed loudspeaker system locations, and multiply this distance measurement in feet by 0.9. As an example, let's say that the delayed loudspeaker system is 80 feet out from the main FOH loudspeaker array; then 0.9 x 80 = 72 milliseconds. Seventy-two milliseconds is the time it takes sound from the main FOH system to reach the location of the delayed loudspeaker, which means that without any delay, the secondary loudspeaker is 72 milliseconds ahead (in time) of the main FOH system.

It is not enough to set the delay for the signal sent to the power amplifier driving the remote loudspeaker at 72 milliseconds, as this will do nothing to maintain the image of the sound as having originated from the front of the sanctuary. There is a concept in audio that says that we pay attention most to that sound that arrives within the first 20 milliseconds. This is sometimes called the precedence effect or the Haas effect. Mr. Haas did testing of human auditory perception, and is more or less the father of Physco-acoustics.

It has been proven that if you add approximately 20 milliseconds to the actual calculated propagation time (when setting the delay for the remote loudspeaker), proper imaging is maintained, and the results are such that no one will even be able to tell that the delayed loudspeaker system is even operating.

It is not a hard and fast rule that the delay setting is set at exactly 20 milliseconds greater, I have seen it set any where from 16 to 26 milliseconds more delay than the calculated direct propagation time. With live music I have observed that certain sounds, particularly the cymbals, can appear as if there is a phase shifter on them if the delay time is exactly 20 milliseconds beyond the calculated propagation time.

Applications where the room is wider

Now let us take a look at applications where the room is wider than in these past examples.

The typical approach in wider rooms is to provide for left and right near field coverage along with a Far Field System. This can be best done with a three-loudspeaker array. The outside loudspeakers are turned upside down to cover the near field left and right seating areas, while the center loudspeaker is mounted right side up. The center loudspeaker is still angled downward somewhat while the outside loudspeakers are angled down about forty degrees farther.

Below is a scanned photograph of a three-loudspeaker array as we just described. This particular array is what we have in our auditorium at the Peavey Dealer Training Center in Meridian, Mississippi. There is also a complete article that covers how this approach can be done with a single power amplifier operated in bridge mode.

Octagon or pie shaped

There are also some church sanctuaries where the actual longest distances are to the left and right rear corners of the church. These rooms are usually more octagon or even pie shaped. In the case of an application such as this, another type of a three-loudspeaker system array can be employed. This time, however, the two outside speakers are to be mounted right side up while the center loudspeaker is mounted upside-down. The outside loudspeakers now provide for the Far Field coverage to the left and right rear corners while the center loudspeaker becomes our Near Field center fill enclosure. However, this approach cannot be driven from a single amplifier operated in bridge mode. In this application the center (Near Field) loudspeaker needs to be operated -6 dB below the level of the two Far Field enclosures.

What about balconies and alcoves or under balcony spaces. All of the above are best addressed as separate acoustic spaces, which they actually are. Any time the Free Field is truncated (or reduced to a smaller space), the acoustics involved are totally different. The Free Field is that portion of the direct field not influenced by the boundaries. Anytime you introduce a new space with smaller dimensions; it is not a good idea to try to provide coverage from the main FOH array. The best approach for these special requirements is to use smaller loudspeaker enclosures with delay, as outlines above for delayed remote loudspeaker systems.

This paper is only intended to be a general guideline of the principles discussed, and is by no means intended as a cookbook solution. If you are to have utmost success with a sound system installation, you need to rely upon someone with solid experience in the design, calibration, and operation of such systems. To do otherwise is to risk the possibility of an expensive short-term experiment in audio. Prayer can be a powerful tool, but it can't fix a poor sound system design.